The present invention is directed to compressive receivers. It finds particular, although not exclusive, application to compressive receivers that employ surface-acoustic-wave (SAW) dispersive delay lines.
Compressive receivers are powerful signal-processing devices. In a compressive receiver, an incoming signal is progressively translated in frequency, and the resultant "chirped" signal is applied to a linear dispersive delay line, i.e., to a delay line whose delay as a function of frequency is linear. The portionality of delay to frequency is the reciprocal of the chirp rate of the frequency translation. As a consequence, the compressive-receiver output is essentially a Fourier transform of the input signal.
Specifically, the output of the linear dispersive delay line takes the form of a highly modulated sinusoidal signal whose frequency is the center frequency of the delay-line input port. The amplitude of the output sinusoidal signal at a given time is indicative of the amplitude of the spectral content of the receiver input signal at a frequency corresponding to that time, and the phase of the output sinusoid is indicative of the phase of that spectral component.
The Fourier transform of an unmodulated single-frequency signal of infinite duration is an impulse in frequency, i.e., a function of infinite height, of infinitesimal width in frequency, and thus of maximum frequency resolution. The response of a compressive receiver to such a signal, however, has a finite width in frequency, because the duration of the signal that the delay line receives in response to a single-frequency input component is finite. The progressive frequency translation occurs repeatedly over successive input-signal records of only finite lengths. Of the chirp-signal component that results from the progressive translation of a single-frequency component in that finite-length record, moreover, only a segment falls within the pass band of the delay line's input filter.
This necessarily finite input length has an effect not only on frequency resolution but also on dynamic range. The Fourier transform of a single frequency f.sub.o modulated by a rectangular (finite-duration) pulse of width T is a Fourier transform of the form [sin(f-f.sub.o)T]/[(f-f.sub.o)T]. That is, the transform is a function having a maximum in a central lobe at f.sub.o whose width is inversely proportional to record duration. The central lobe is bracketed by minima beyond which local maxima of decreasing amplitude occur in "sidelobes." These sidelobes tend to limit the dynamic range of the compressive receiver; transforms of smaller signals whose magnitudes fall below that of the largest sidelobe of the highest-magnitude signal must be ignored since they cannot be distinguished from sidelobes.
One approach to reducing the adverse effects of sidelobes is to filter the input of the dispersive delay line with a Gaussian filter, which imposes a Gaussian, instead of a rectangular, envelope on the chirp signal that results from a narrow-band input. The result, if all other components of the receiver were ideal, would be a Gaussian output envelope, i.e., one that diminishes monotonically on both sides of the maximum and thus does not produce the sidelobes that result from abrupt interruptions of the input record.
Unfortunately, the other components are not ideal, and certain of their inaccuracies manifest themselves as sidelobes, which reduce the dynamic range from that of an ideal Gaussian-envelope system. The most important of these inaccuracies is the departure of the linear dispersive delay line from precise linearity.
This dynamic-range reduction is particularly pronounced in an intermediate range of frequencies between 30 MHz and 1 GHz. In the region below about 30 MHz, the dispersive delay line is typically embodied in a bulk acoustic delay line, which can be made highly linear; dynamic ranges in excess of 60 db are routinely achieved in compressive receivers that employ such delay lines. In the microwave region above approximately 1 GHz, surface-electromagnetic-wave delay lines can be used that result in similar dynamic ranges.
However, in the intermediate range between approximately 30 MHz and 1 GHz, it is necessary to resort to surface-acoustic-wave dispersive delay lines, and it has not typically been feasible to make such delay lines linear enough to achieve dynamic ranges much in excess of 30 db.